A classical and a relativistic law of motion for SN1987A

TL;DR

This paper develops differential equations modeling the motion of SN1987A's expanding shell using classical and relativistic physics, considering various circumstellar medium density profiles, and fits the models to 23 years of observational data.

Contribution

It introduces new differential equations for modeling supernova expansion with diverse density profiles and provides analytical and numerical solutions fitted to real observational data.

Findings

Models accurately fit 23 years of SN1987A data.

Relativistic effects are significant in early expansion phases.

Different density profiles influence the supernova's expansion dynamics.

Abstract

In this paper we derive some first order differential equations which model the classical and the relativistic thin layer approximations in the presence of a circumstellar medium with a density which is decreasing in the distance $z$ from the equatorial plane. The circumstellar medium is assumed to follow a density profile with $z$ of hyperbolic type, power law type, exponential type or Gaussian type. The first order differential equations are solved analytically, or numerically, or by a series expansion, or by Pad\'e approximants. The initial conditions are chosen in order to model the temporal evolution of SN 1987A over 23 years. The free parameters of the theory are found by maximizing the observational reliability which is based on an observed section of SN 1987A.